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Register a new userStrong averaging principle for a class of slow-fast singular SPDEs driven by $alpha$-stable process
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In this paper, the strong averaging principle is researched for a class of H{o}lder continuous drift slow-fast SPDEs with $alpha$-stable process by the Zvonkins transformation and the classical Khasminkiis time discretization method. As applications, an example is also provided to explain our result.
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In this paper, the averaging principle is studied for a class of multiscale stochastic partial differential equations driven by $alpha$-stable process, where $alphain(1,2)$. Using the technique of Poisson equation, the orders of strong and weak convergence are given $1-1/alpha$ and $1-r$ for any $rin (0,1)$ respectively. The main results extend Wiener noise considered by Br{e}hier in [6] and Ge et al. in [17] to $alpha$-stable process, and the finite dimensional case considered by Sun et al. in [39] to the infinite dimensional case.
In this paper, we first study the well-posedness of a class of McKean-Vlasov stochastic partial differential equations driven by cylindrical $alpha$-stable process, where $alphain(1,2)$. Then by the method of the Khasminskiis time discretization, we prove the averaging principle of a class of multiscale McKean-Vlasov stochastic partial differential equations driven by cylindrical $alpha$-stable processes. Meanwhile, we obtain a specific strong convergence rate.
In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we show that the slow component strongly converges to the solution of the associated averaged equation. In particular, the corresponding convergence rates are also obtained. The main results can be applied to demonstrate the averaging principle for various McKean-Vlasov nonlinear SPDEs such as stochastic porous media type equation, stochastic $p$-Laplace type equation and also some McKean-Vlasov stochastic differential equations.
In this paper, we study a class of slow-fast stochastic partial differential equations with multiplicative Wiener noise. Under some appropriate conditions, we prove the slow component converges to the solution of the corresponding averaged equation with optimal orders 1/2 and 1 in the strong and weak sense respectively. The main technique is based on the Poisson equation.
In this paper, we study a system of stochastic partial differential equations with slow and fast time-scales, where the slow component is a stochastic real Ginzburg-Landau equation and the fast component is a stochastic reaction-diffusion equation, the system is driven by $alpha$-stable process with $alphain (1,2)$. Using the classical Khasminskii approach based on time discretization and the techniques of stopping times, we show that the slow component strong converges to the solution of the corresponding averaged equation under some suitable conditions.
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